Question

F(x) = x^2 + 4x + 20 find the real roots. take your time if you want :)

Answer 1

No real roots

`x = -2 + 4i, x = -2 - 4i`

Explanation:

Hello!

We can solve the quadratic by using the Quadratic Formula.

Standard form of a Quadratic:
`ax^2 + bx + c = 0`

Quadratic Equation:
`x = (-b\pm√(b^2 - 4ac))/(2a)`

Given our Equation:
`f(x) = x^2 + 4x + 20`

• a = 1
• b = 4
• c = 20

Set the equation to 0 and solve using the formula.

Solve

• 
  `x = (-b\pm√(b^2 - 4ac))/(2a)`
• 
  `x = (-4\pm√(4^2 - 4(1)(20)))/(2(1))`
• 
  `x = (-4\pm√(16 - 80))/(2)`
• 
  `x = (-4\pm√(-64))/(2)`
• 
  `x = (-4\pm8i)/(2)`
• 
  `x = -2 + 4i, x = -2 - 4i`

There are no real roots to the quadratic.